Without a majority in parliament, Mr Barnier – the fifth French prime minister in seven years – used special powers to force through the budget without a vote.
Furious opposition parties have now said they will back a no-confidence motion to oust him.
Two motions of no-confidence will be debated in the National Assembly in Paris from 4pm on Wednesday, with a vote at around 7pm.
Mr Barnier could be out of power by Thursday – the three-month anniversary of when he was appointed.
No French government has been forced out by such a vote since 1962 and it would make Mr Barnier the shortest-serving prime minister in the history of the Fifth Republic.
Bernard Cazeneuve spent the least amount of time in the role – just over five months – while Mr Barnier’s predecessor Gabriel Attal held the post for eight months.
Mr Macron is also facing calls to resign as a recent poll showed well over half of the French people would be in favour of him quitting if Mr Barnier’s government falls.
Mr Barnier’s brief was to rescue the French economy by getting the GDP deficit ratio back below 3%.
To do that, his budget included deep cuts to public spending totalling £33billion (€40billion) and steep tax rises amounting to £16billion (€20billion).